Average Error: 6.4 → 2.4
Time: 9.0s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x + \left(z - t\right) \cdot \frac{y}{a}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
x + \left(z - t\right) \cdot \frac{y}{a}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) a)))
↓
(FPCore (x y z t a) :precision binary64 (+ x (* (- z t) (/ y a))))
double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / a);
}
↓
double code(double x, double y, double z, double t, double a) {
	return x + ((z - t) * (y / a));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.4
Target0.7
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 6.4

    \[x + \frac{y \cdot \left(z - t\right)}{a}\]
  2. Using strategy rm

  3. Applied clear-num_binary64_116716.5

    \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{y \cdot \left(z - t\right)}}}\]

  4. Simplified6.5

    \[\leadsto x + \frac{1}{\color{blue}{\frac{a}{\left(z - t\right) \cdot y}}}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity_binary64_116726.5

    \[\leadsto x + \frac{1}{\frac{\color{blue}{1 \cdot a}}{\left(z - t\right) \cdot y}}\]

  7. Applied times-frac_binary64_116782.5

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{z - t} \cdot \frac{a}{y}}}\]

  8. Applied add-sqr-sqrt_binary64_116942.5

    \[\leadsto x + \frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{\frac{1}{z - t} \cdot \frac{a}{y}}\]

  9. Applied times-frac_binary64_116782.6

    \[\leadsto x + \color{blue}{\frac{\sqrt{1}}{\frac{1}{z - t}} \cdot \frac{\sqrt{1}}{\frac{a}{y}}}\]

  10. Simplified2.6

    \[\leadsto x + \color{blue}{\left(z - t\right)} \cdot \frac{\sqrt{1}}{\frac{a}{y}}\]

  11. Simplified2.4

    \[\leadsto x + \left(z - t\right) \cdot \color{blue}{\frac{y}{a}}\]

  12. Final simplification2.4

    \[\leadsto x + \left(z - t\right) \cdot \frac{y}{a}\]

Reproduce

herbie shell --seed 2021050 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

  (+ x (/ (* y (- z t)) a)))